%Solution1.m
E =eye(3)
u = E(:,1)
E(3,1) = 5
v = E*u
A = ones(3) + eye(3)
b = A(:,3)
C = inv (A)

x = A\b
x = C*b

%This is a comment
%help slsh
%last line was a comment
help slash
%"help slash" last line was ignored :O
%but it works in the console
%Edit : it works! I actually forgot to save the file :p

u = [2 4 5]
v = [2;4;5]
v = [2 4 5]'
w= 2:5
u= 1:2:7
A = [1 2 3; 4 5 6]
A = [1 2 3
4 5 6]
%both last two commands work as expected >.>
B = [1 2 3; 4 5 6]'
%created [1 2 3; 4 5 6] first, transposed it and put it into B
diag(v)
disp("toeplitz(v):")
toeplitz(v)
disp("toeplitz(w):")
toeplitz(w)
disp("toeplitz(w,v):")
toeplitz(w,v)
disp("ones(5)")
ones(5)
zeros(7)
eye(10)
rand(5)
randn(5)
disp("ones (4,7)")
ones(4,7)
disp("size(A):")
size(A)
%probably next command shall make ones with 2 rows and 3 collumns
disp("ones size(A):")
ones (size(A))

%it did!
zeros(size(A))
%will next command excecute? A is 2x3
eye(size(A))
%IT DID!
A(3,2) = 7
%A NEW ROW IS CREATED!
 %  --> A(3,:) = w
 %Error occured since w is 1 X 4
 A(3,:) = v

% A(:,2) = w error occured since w is 1X4 but col 2 of A has 3 elements
A([2 3],:) = A([3 2], :)

A(2,2)
A(1,:)
A(:,3)
A(1:3,2:3)
A(:)
triu(A)
tril(A)
disp("B:")
B
A*B
%A.*B is not possible because A is 3x3 where B is 3x2
A.*A'
inv (A)
pinv(A)
A\v
inv(A)*v
det(A)
rank(A)
size(A)
trace(A)
null(A)
orth(A)


E = eye(4)
E(2,1) = -3
E*(ones(4))

[L,U,P] = lu(A)
e = eig(A)
[S,E] = eig(A)
[Q,R] = qr(A)

plot(v)
x= A(:,2)
y = L(:,1)
disp("plot");
plot(x,y)
disp("plot red +");
plot (x,y,'r+:')
disp("plot --");
plot (x,y,'--')
plot(x,y,'o')
loglog(x,y)